210 1998 Elisabeth Larsson and Leif Abrahamsson bette@tdb.uu.se Helmholtz and PE solutions to a benchmark problem in ocean acoustics
Abstract
The Helmholtz equation (HE) describes wave propagation in
applications such as acoustics and electromagnetics. For realistic
problems, solving the HE is often too expensive. Instead
approximations like the parabolic wave equation (PE) are used.
For low-frequency shallow water environments, one persistent problem is to
assess the accuracy of the PE model. In this work, a recently developed HE
solver that can handle a smoothly varying bathymetry, variable material
properties, and layered materials, is used for an investigation of the errors
in PE solutions. In the HE solver, a preconditioned Krylov subspace method
is applied to the discretized equations. The preconditioner combines domain
decomposition and fast transform techniques. A benchmark problem with
upslope--downslope propagation over a penetrable lossy seamount is solved.
The numerical experiments show that, for the same bathymetry, a soft and slow
bottom gives very similar HE and PE solutions, whereas the PE model is far
from accurate for a hard and fast bottom. A first attempt to estimate the
error is made by computing the relative deviation from the energy balance
for the PE solution. This measure gives an indication of the magnitude of
the error, but cannot be used as a strict error bound.